TIDES (AS. tid, ma. et, Ger. Zeit, time; connected with Skt. e-diti, boundless, and ulti mately with Eng. lime). The daily rising and falling of the waters of the ocean. When the water has reached the highest point it is high water, and at its lowest point law water. The rising of the water is called flood, the falling ebb. Tides are caused by the gravitational at traction or pull of the sun and moon upon the water, and upon the earth itself. The moon, being so much nearer than the sun, is of course the principal cause. When the moon is directly over a given place it pulls the water under it, and thus tends to heap up a tidal wave just under the moon. At the same time it is pulling the earth itself; but it pulls the water more than the earth underneath, simply because the moon is nearer to the water on the surface than it is to the solid earth behind it. For we must remem ber that, according to Newton's law of attraction, the pull decreases rapidly when the body pulled is removed to a greater distance. But this reason also makes the attraction exerted upon the solid earth greater than that affecting the mass of water upon the side of the earth opposite to the moon. This water, being still farther away than is the solid earth, gets the least pull of all. The earth is, so to speak, pulled away from that part of the ocean that is opposite the moon, instead of directly under it. This causes another distinct heaping up of water opposite the moon, giving us a second tidal wave. There should he, therefore, two lunar tidal-wave crests, one directly under the moon and tire other on the side of the earth opposite the moon. This explanation is modified somewhat on account of the attraction of the sun, which at times tends to increase, and again at times to diminish, the lunar tide. We thus get the high tides of new and full moon (spring tides) and the low tides of certain other ages of the moon (neap tides). And the double tidal wave explains why there are two high tides and two low tides every twenty-four hours. This ex planation is called the 'equilibrium' theory of the tides. It is very plausible, but unfortunately it fails to agree with observed facts, though it is nevertheless of great use in leading up to a better theory. Under the equilibrium theory we should expect high water at any place about the time when the moon, as astronomers say, passes the meridian. This time might be modified by
the solar effects, but only to a rather small amount easily calculated. Unfortunately, this is not in accord with observation. There are places where the high water comes as much as six hours away from the meridian passage of the moon. In other words, the equilibrium theory is at times in error by the maximum possible amount. The trouble is that it tells us what would happen if the forces governing the tides had plenty of time to act. But the turning of the earth on its axis continually presents a new meridian to the moon, so that the tidal-wave crest is always following the moon, ever trying to be highest directly under it. Thus what should occur under the equilibrium theory is greatly modified by the theory of the motion of fluid wares. This leads them to the 'dynamical' theory of the tides.
A consideration of the subject is much simpli fied by assuming a condition of things that does not really exist in nature. Let us imagine a canal full of water encircling the earth at the equator. Sir Isaac Newton was the first to in vestigate what would happen to a wave set in motion in such a canal. It can be shown mathe matically that the speed at which such a wave would travel depends simply on the depth of the canal. The deeper the canal, the greater the speed of the wave. This is. of course, very important, and shows what a perfectly free wave would do under such simplified conditions. It can even be computed that if the canal were l33.1 miles deep, the wave would travel round the earth in exactly twenty-four hours. Now, it is the tendency of the sun and moon to set such a free wave in motion at each instant of time; and these go on traveling along more or less like the supposed simple wave in the canal. If the ocean were miles deep, the waves would have a period of one day; and the new free waves forming all the time would reinforce the old ones, leading to an enormous tidal accumulation. Fortunate ly, the ocean is much less than lnimiles deep, and the waves travel much more slowly than once a day. It may happeu, therefore, that as the waves travel around the earth, their speed may be such that we shall find a wave hollow instead of a wave crest under the moon. Thus, the modification of the equilibrium theory by the wave motion may at times completely reverse things, giving us low tide when we should ex pect high tide.